EP1576763B1 - Secret sharing scheme using exclusive or calculation - Google Patents

Secret sharing scheme using exclusive or calculation Download PDF

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Publication number
EP1576763B1
EP1576763B1 EP03780959.7A EP03780959A EP1576763B1 EP 1576763 B1 EP1576763 B1 EP 1576763B1 EP 03780959 A EP03780959 A EP 03780959A EP 1576763 B1 EP1576763 B1 EP 1576763B1
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data
divided
original
partial data
random number
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EP1576763A2 (en
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Toshihiko c/o NTT COMMUNICATIONS CORP. OGIHARA
Susumu c/o NTT COMMUNICATIONS CORP. NOMURA
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NTT Communications Corp
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
    • H04L9/085—Secret sharing or secret splitting, e.g. threshold schemes

Definitions

  • the present invention relates to data division method and device which are effective in the case of maintaining data in division in order to secure secrecy and safety of the data, and more particularly to data division method and device which divide original data into a desired number of divided data according to a desired processing- unit bits.
  • the original data S is divided into n sets of divided data, and the original data S can be recovered by collecting at least certain number x sets of the divided data among the n sets of the divided data, but the original data S cannot be recovered by collecting only x-1 sets of the divided data. Consequently, the original data S is not leaked even if as many as x-1 sets of the divided data are stolen, and the original data S can be recovered even if as much as n-x sets of the divided data are lost or destroyed.
  • a storage drive reads raw data, including error correction codes, from the media and encrypts the data by exclusive OR-ing each error correction code block with a new error correction code block which was generated using random data and the same error correction code scheme.
  • WO 99/41877 there is described a method and arrangement for ciphering information transfer.
  • the approach is applied to TDMA cellular system offering broadband circuit switched services.
  • Information is to be ciphered in a transmission burst being divided into at least two blocks and the blocks are ciphered in ways that are not identical with each other. This increases reliability as the amount of information encoded using one and the same ciphering algorithm and key is smaller. Further, the reliability of ciphering may be varied by changing the number and/or size of information blocks in a burst.
  • US-A-6,088,449 describes a tri-signature security architecture system and method.
  • an encryption system and method utilizes a bit stream called a 'master signature', which is divided into bytes with each byte being assigned a byte address.
  • a portion of the master signature called an 'access signature' is randomly selected to encode the message to be transmitted.
  • Both a sender and a receiver have the same access signature. In particular, by using a part of the access signature at the sender and the receiver, the sender and the receiver can encrypt and decrypt the message using the same portion of the access signature.
  • US 2001/0012362 A1 describes a data encryptor/decryptor using variable in-place I/O.
  • a computer implemented process for data encryption or data decryption using an ordered element per matrix array wherein a computer includes a central processing unit which accesses a random access memory to control an input/output device.
  • the described process allows for encryption of data prior to transmission and for decryption of encrypted data.
  • Fig.1 shows a configuration of a system including the data division device for realizing the data division method according to one embodiment of the present invention.
  • a division device 1 is connected to a network 3, and operated to divide the original data S into divided data according to an original data division request from a terminal 5 which made an access to this network 3 and deposit a plurality of divided data into a plurality of deposit servers 7a, 7b and 7c through the network 3.
  • the division device 1 divides the original data S from the terminal 5 into three divided data D(1), D(2) and D(3), and deposit them into the plurality of deposit servers 7a, 7b and 7c, respectively.
  • the division device is operated to acquire the plurality of the divided data D(1), D(2) and D(3) from the deposit servers 7 through the network 3 according to an original data recovery request from the terminal 5 which made an access through the network 3, recover the original data S from the plurality of the divided data D(1), D(2) and D(3), and transmit the original data S to the terminal 5 through the network 3.
  • the division device 1 comprises a divided data generation unit 11 for generating a plurality of divided data D from the original data S, an original data recovery unit 13 for recovering the original data S from the plurality of the divided data D, a random number generation unit 15 for generating random number R which is used in generating the the plurality of the divided data D from the original data S, and a data transmission and reception unit 17 for transmitting the plurality of the divided data D generated by the divided data generation unit 11 to the plurality of the deposit servers 7a, 7b and 7c through the network 3, or receiving the plurality of the divided data D from the plurality of the deposit servers 7a, 7b and 7c through the network 3.
  • the original data is divided into the divided data in a desired number of division according to a desired processing unit bit length, and this processing unit bit length can be set to an arbitrary value.
  • the original data is partitioned into original partial data of the processing unit bit length, and divided partial data in a number less than the number of division by one are generated from each original partial data, so that when the bit length of the original data is not an integer multiple of (number of division - 1) times the processing unit bit length, the bit length of the original data is adjusted to become an integer multiple of (number of division - 1) times the processing unit bit length by filling up the tail of the original data by 0, for example.
  • the random number mentioned above is generated by the random number generation unit 15 as (number of division - 1) sets of random number partial data having a bit length equal to the processing unit bit length, in correspondence to (number of division - 1) sets of the original partial data.
  • the random number is generated and partitioned by the processing unit bit length as (number of division - 1) sets of the random number partial data having a bit length equal to the processing unit bit length.
  • the original data are divided into the divided data in the desired number of division according to the processing unit bit length, and each one of these divided data is also generated as (number of division - 1) sets of divided partial data having a bit length equal to the processing unit bit length in correspondence to (number of division - 1) sets of the original partial data.
  • each one of the divided data is generated and partitioned by the processing unit bit length as (number of division - 1) sets of the divided partial data having a bit length equal to the processing unit bit length.
  • the original data, the random number data, the divided data, and their constituents i.e. the original partial data, the random number partial data and the divided partial data, can be expressed as follows.
  • This embodiment is characterized by realizing the division of the original data by carrying out the exclusive OR (XOR) calculation of the original partial data and the random number partial data with respect to the plurality of partial data in the processing unit bit length as described above, or more specifically, by using a definition formula formed by the exclusive OR (XOR) calculation of the original partial data and the random number partial data.
  • XOR exclusive OR
  • this embodiment uses the exclusive OR (XOR) calculation which is a bit calculation suitable for the computer processing so that it does not require a high speed and high performance calculation processing power, the divided data can be generated for a large capacity data by repeating the simple calculation processing, and the memory capacity required for maintaining the divided data becomes smaller than the capacity that is linearly proportional to the number of division.
  • the divided data can be generated by the stream processing in which the calculation processing is carried out sequentially from the top of the data in units of a prescribed arbitrary length.
  • a, b and c represent bit sequences of the same length, and 0 represents a bit sequence consisting of "0" which has the same length as a, b and c.
  • Q(j, i, j) is defined as follows.
  • this is a matrix such as the following.
  • E 3 3 1 0 0 0 1 0 0 0 1
  • E 4 4 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1
  • the user of the division device 1 of this embodiment makes an access to the division device 1 from the terminal 5 through the network 3 and transmits the original data S to the division device 1.
  • the the data transmission and reception unit 17 of the division device 1 receives the original data S from the terminal 5 and supplies it to the division device 1 (step S201 of Fig. 2 ).
  • the original data S is assumed to be 16 bits given by "10110010 00110111".
  • D(1), D(2) and D(3) are all data with the 16 bits length which is the same bit length as the original data.
  • the processing unit bit length b to be used in dividing the original data S is determined as 8 bits, and the random number R in 16 bits which is the same bit length as the original data S is generated at the random number generation unit 15 (step S205).
  • This processing unit bit length b may be specified by the user from the terminal 5 to the division device 1, or may be a value predetermined by the division device 1.
  • the processing unit bit length b can be an arbitrary number of bits but here it is assumed to be 8 bits by which the original data S is divisible. Consequently, when the above described original data S "10110010 00110111" in 16 bits is divided by the processing unit bit length of 8 bits, the resulting two original partial data S(1) and S(2) are given by "10110010" and "00110111".
  • the bit length of the original data S is an integer multiple of 8x2 or not is judged, and if it is not an integer multiple, the tail of the original data S is filled up by 0 to make it an integer multiple of 8 ⁇ 2.
  • the following divided data D are generated.
  • the definition formula for generating the divided partial data D(1,1) is S(1)*R(1)*R(2)
  • the definition formula for generating the divided partial data D(1,2) is S(2)*R(1)*R(2)
  • the definition formula for generating the divided partial data D(2,1) is S(1)*R(1)
  • the definition formula for generating the divided partial data D(2,2) is S(2)*R(2)
  • the definition formula for generating the divided partial data D(3,1) is R(1)
  • the definition formula for generating the divided partial data D(3,2) is R(2).
  • the table shown in Fig. 4 also shows a general definition formula in the case where m > 0 is an arbitrary integer.
  • each divided partial data D(i,j) is generated by the following definition formula.
  • the first divided partial data D(1,1) is defined by the above described formula S(1)*R(1)*R(2)
  • the second divided partial data D(1,2) is defined by the above described formula S(2)*R(1)*R(2).
  • the general form is S(j)*R(j)*R(j+1) for D(1,j) and S(j+1)*R(j)*R(j+1) for the D(1,j+1) (where j is assumed to be an odd number).
  • the first divided partial data D(2,1) is defined by the above described formula S(1)*R(1)
  • the second divided partial data D(2,2) is defined by the above described formula S(2)*R(2).
  • the general form is S(j)*R(j) for D(2,j) and S(j+1)*R(j+1) for the D(2,j+1) (where j is assumed to be an odd number).
  • the first divided partial data D(3,1) is defined by the above described formula R(1)
  • the second divided partial data D(3,2) is defined by the above described formula R(2).
  • the general form is R(j) for D(3,j) and R(j+1) for the D(3,j+1) (where j is assumed to be an odd number).
  • bit length of S, R, D(1), D(2) and D(3) is assumed to be 16 bits, but it is possible to generate the divided data D(1), D(2) and D(3) from the original data S of any bit length by repeating the above described division processing from the top of the data.
  • the processing unit bit length b can be arbitrary, and it is applicable to the original data S of arbitrary bit length by repeating the above described division processing for each length of bx2 sequentially from the top of the original data S, or more specifically to the original data S with a bit length which is an integer multiple of the processing unit bit length b ⁇ 2.
  • bit length of the original data S is not an integer multiple of the processing unit bit length b ⁇ 2
  • the user makes an access to the division device 1 from the terminal 5 through the network 3, and requests the recovery of the original data S through the data transmission and reception unit 17 of the division device 1.
  • the division device 1 Upon receiving this recovery request for the original data S, as the division device 1 knows that the divided data D(1), D(2) and D(3) corresponding to this original data S are deposited in the deposit servers 7a, 7b and 7c, the division device 1 acquires the divided data D(1), D(2) and D(3) from the deposit servers 7a, 7b and 7c through the network 3, and recovers the original data S from the acquired divided data D(1), D(2) and D(3) as follows.
  • the first original partial data S(1) can be generated from the divided data D(2,1) and D(3,1) as follows.
  • D(2,1) is "00000011” and D(3,1) is “10110001" so that S(1) becomes "10110010”.
  • the second original partial data S(2) can be generated from the other divided partial data as follows.
  • D(2,2) is "00000010” and D(3,2) is "00110101" so that S(2) becomes "00110111”.
  • the random number R is assumed to be data with the same bit length as S, D(1), D(2) and D(3) in the above, but the random number R can have a bit length shorter than a bit length of the original data S and this random number R with a shorter bit length can be used repeatedly in the generation of the divided data D(1), D(2) and D(3).
  • the divided data D(3) is generated solely from the random number R, so that there is no need to deposit the random number R repeatedly for the divided data D(3).
  • the bit length of the original data S is 1600 bits (200 bytes)
  • the random number is repetition of arbitrarily selected 160 bits (20 bytes) data.
  • D(3) is generated by defining the divided partial data D(3,j) as the random number partial data R(j), but in this case it is sufficient to store only up to D(3,20). Namely, the length of D(3) becomes 1/10 of D(1) and D(2). Consequently, the total amount of data to be stored has been three times the data amount of the original data S in the previous embodiment, but in this embodiment, this total amount can be reduced to 2.1 times the data amount of the original data S.
  • the length of the data in the repeated portion of the random number R should preferably be appropriately long enough, because if it is too short, the random number R may possibly be decoded from D(1) or D(2) alone.
  • the pseudo-random number generation algorithm is used in order to generate the random number R, for example.
  • the random number There are two types of the random number including a truly random number which is generated by using a physical phenomenon in nature, and a pseudo-random number which is generated by using a computer algorithm or the like.
  • the truly random number can be generated by throwing dice many times or utilizing a physical phenomenon such as noises, but it requires too much time and effort so that the pseudo-random number is used instead.
  • the pseudo-random number is generated from a seed (information to becomes a seed of the random number generation) of appropriate length according to a deterministic algorithm.
  • the longer random number can be obtained from a shorter seed, for example.
  • the length of the seed can be 128 bits, 160 bits or longer, for example.
  • the concrete examples of the standardized pseudo-random number includes ANSI X9.42 and FIPS 186-2 (see "http://www.ipa.go.jp/security/enc/ CRYPTREC/fy15/cryptrec20030425_spec01.html", for example).
  • the random number R with a length equal to the bit length of the original data S is generated by inputting a seed of 160 bits, D(1) and D(2) are generated from S and R as described above, and the seed of 160 bits is stored and managed for D(3) rather than storing R.
  • the number of bits that need to be stored and managed for D(3) can be reduced to 160 bits even when the bit length of the original data S becomes long, so that the total amount of data to be stored can be suppressed.
  • the random number R with a length equal to the bit length of the original data S is generated again from the seed of 160 bits stored for D(3), and the original data S can be recovered by using this R and D(1) or D(2) as described above.
  • the embodiments described above are directed to the case where the original data is divided into three, and the original data can be recovered from two divided data, but it is also possible to set the number of division n to be greater than 3, and recover the original data from a number of divided data less than n.
  • the user transmits the original data S by making an access to the division device 1 from the terminal 5, and the data transmission and reception unit 17 of the division device 1 receives the original data S from the terminal 5 and supplies it to the division device 1 (step S301).
  • the user specifies the number of division n as 4 to the division device 1 from the terminal 5 (step S303).
  • This number of division n may be a value predetermined by the division device 1.
  • the processing unit bit length b is determined as 8 bits, for example (step S305).
  • step S307 whether the bit length of the original data S is an integer multiple of 8x3 or not is judged, and if it is not an integer multiple, the tail of the original data S is filled up by 0 (step S307).
  • a variable m which indicates an integer multiple is set to 0 (step S309).
  • the random number with a length equal to 8 bits generated by the random number generation unit 15 is set as the random number partial data R(3 ⁇ m+j) while changing the variable j from 1 to 3, such that three sets of the random number partial data R(1), R(2) and R(3) resulting from the division of the random number R by the processing unit bit length are generated (step S315).
  • the following divided data D are generated.
  • the definition formula for generating the divided partial data D(1,1) is S(1)*R(1)*R(2)*R(3)
  • the definition formula for generating the divided partial data D(1,2) is S(2)*R(1)*R(2)*R(3)
  • the definition formula for generating the divided partial data D(1,3) is S(3)*R(1)*R(2)*R(3)
  • the definition formula for generating the divided partial data D(2,1) is S(1)*R(1)*R(2)
  • the definition formula for generating the divided partial data D(2,2) is S(2)*R(2)*R(3)
  • the definition formula for generating the divided partial data D(2,3) is S(3)*R(1)*R(3)
  • the definition formula for generating the divided partial data D(3,1) is S(1)*R(1)
  • the definition formula for generating the divided partial data D(3,2) is S(2)*R(2)
  • the definition formula for generating the divided partial data D(3,3) is S(3)*R(3)
  • the definition formula for generating the divided partial data D(4,1) is R(1)
  • the deposit servers 7 there are three deposit servers 7 shown in Fig. 1 , but it is preferable to increase the deposit servers according to the number of division such that different divided data can be deposited into different deposit servers.
  • each divided partial data D(i,j) is generated by the following definition formula.
  • each one of (n-1) sets of the original partial data, (n-1) sets of the random number partial data, n sets of the divided data D, and (n-1) sets of divided partial data of each divided data will be denoted as S(j), R(j), D(j), and D(i,j).
  • each original partial data S(j) is generated as b bits of data from b ⁇ (j-1)+1-th bit of the original data S while changing the above described variable j from 1 to n-1.
  • U[n,n] is an n ⁇ n upper triangular matrix
  • P[n,n] is an n ⁇ n rotation matrix
  • c(j,i,k) is defined as a value of the i-th row and the k-th column of an (n-1) ⁇ (n-1) matrix U[n-1,n-1] ⁇ P[n-1,n-1] ⁇ (j-1).
  • the processing for recovering the original data S from the divided data D(1), D(2), D(3) and D(4) that are generated by dividing the original data S into four as described above will be described with reference to Fig. 6 .
  • the random number R(j+2) can be obtained by calculating D(1,j)*D(2,j), and similarly, the random number R(j) can be obtained by calculating D(1,j+1)*D(2,j+1) and the random number R(j+1) can be obtained by calculating D(1,j+2)*D(2,j+2).
  • S(j+1) can be obtained by calculating either D(1,j+1)*R(j)*R(j+1)*R(j+2) or D(2,j+1)*R(j+1)*R(j+2)
  • S(j+2) can be obtained by calculating either D(1,j+2)*R(j)*R(j+1)*R(j+2) or D(2,j+2)*R(j)*R(j+2).
  • R(j), R(j+1) and R(j+2) are obtained, and then S(j), S(j+1) and S(j+2) can be obtained by the XOR calculation of D(2,j), D(2,j+1), D(2,j+2) or D(3,j), D(3,j+1), D(3,j+2) with R(j), R(j+1), R(j+2).
  • S can be obtained from D(1) and D(4), or D(2) and D(4), or D(3) and D(4).
  • D(4) us defined by R itself, so that R(j), R(j+1) and R(j+2) can be obtained from D(4) without any calculation.
  • S(j), S(j+1) and S(j+2) can be obtained by the XOR calculation of D(1,j), D(1,j+1), D(1,j+2) with R(j), R(j+1), R(j+2).
  • S can be recovered from two arbitrary divided data D(1) and D(2), or D(2) and D(3), or D(4) and any arbitrary one of the divided data D(1), D(2) or D(3), for which a difference in the number of calculation is one. Namely, if three divided data among the four divided data are acquired, at least one of the above described cases can be realized so that the original data can be recovered from arbitrary three divided data among the four divided data.
  • Fig. 7 shows a table indicating the divided data and the definition formula in the case of the division into five.
  • the original data can be recovered from (n+1)/2 sets of the divided data if n is an odd number, or (n/2)+1 sets of the divided data if n is an even number.
  • This number of sets is obtained as one plus the maximum number that can be selected when there are n divided data, the adjacent divided data are not to be selected and the n-th divided data is not to be selected.
  • the maximum number plus one sets of the divided data are acquired, two divided data for which a difference in the number of calculation is one or the n-th divided data and any other divided data are surely contained among them, so that this gives the number of divided data that are necessary for the recovery.
  • the user transmits the original data S by making an access to the division device 1 from the terminal 5, and the data transmission and reception unit 17 of the division device 1 receives the original data S from the terminal 5 and supplies it to the division device 1 (step S401). Then, the user specifies the number of division n (arbitrary integer n ⁇ 3) to the division device 1 from the terminal 5 (step S403). This number of division n may be a value predetermined by the division device 1. Also, the processing unit bit length b is determined (step S405), where n is an arbitrary integer greater than zero.
  • bit length of the original data S is an integer multiple of b ⁇ (n-1) or not is judged, and if it is not an integer multiple, the tail of the original data S is filled up by 0 (step S407). Also, a variable m which indicates an integer multiple is set to 0 (step S409).
  • step S411 whether b ⁇ (n-1) bits of data from the b ⁇ (n-1) ⁇ m+1-th bit of the original data S exist or not is judged. As a result of this judgement, if the data do not exist, the processing will proceed to the step S421, but currently the variable m is set to 0 at the step S409 and the data exist so that the processing proceeds to the step S413.
  • b bits of data from b ⁇ ((n-1) ⁇ m+j-1)+1-th bit of the original data S is set as the original partial data S((n-1) ⁇ m+j) while changing the variable j from 1 to n-1, such that (n-1) sets of the original partial data S(1), S(2), ⁇ , S(n-1) resulting from the division of the original data S by the processing unit bit length b are generated.
  • the random number with a length equal to the processing unit bit length b generated by the random number generation unit 15 is set as the random number partial data R((n-1) ⁇ m+j) while changing the variable j from 1 to n-1, such that (n-1) sets of the random number partial data R(1), R(2), ⁇ , R(n-1) resulting from the division of the random number R by the processing unit bit length b are generated (step S415).
  • each divided partial data D(i,(n-1) ⁇ m+j) that constitutes each one of the plurality of the divided data D(i) is generated according to the definition formula for generating the divided data as shown in the step S417, while changing the variable i from 1 to n and changing the variable j from 1 to n-1 for each variable i.
  • the following divided data D are generated.
  • step S411 the processing proceeds from the step S411 to the step S421, where the divided data D generated as described above are transmitted to the deposit servers 7 respectively, from the data transmission and reception unit 17 of the division device 1 through the network 3, such that they are deposited in the respective deposit servers 7 and then the division processing is finished.
  • the deposit servers 7 there are three deposit servers 7 shown in Fig. 1 , but it is preferable to increase the deposit servers according to the number of division such that different divided data can be deposited into different deposit servers.
  • the user supplies the original data S by making an access to the division device 1 from the terminal 5 (step S501). Then, thei division n as 2 to the division device 1 from the terminal 5 (step S503). This number of division n may be a value predetermined by the division device 1. Also, the processing unit bit length b is determined as 8 bits (step S505). Next, whether the bit length of the original data S is an integer multiple of 8 or not is judged, and if it is not an integer multiple, the tail of the original data S is filled up by 0 (step S507). Also, a variable m which indicates an integer multiple is set to 0 (step S509).
  • step S511 whether 8 bits of data from the 8xm+1-th bit of the original data S exist or not is judged. As a result of this judgement, if the data do not exist, the processing will proceed to the step S521, but currently the variable m is set to 0 and the data exist so that the processing proceeds to the step S513.
  • step S513 8 bits of data from 8 ⁇ m+1-th bit of the original data S is set as the original partial data S(m+1), such that the original partial data S(1) is generated.
  • the random number with a length equal to 8 bits generated by the random number generation unit 15 is set as the random number partial data R(m+1) such that the random number partial data R(1) is generated (step S515).
  • each divided partial data D(i,m+1) and D(2,m+1) that constitutes each one of the divided data D are generated according to the definition formula for generating the divided data as shown in the step S517.
  • step S511 the processing proceeds from the step S511 to the step S521, where the divided data D(1) and D(2) generated as described above are transmitted to the deposit servers 7 respectively, from the data transmission and reception unit 17 of the division device 1 through the network 3, such that they are deposited in the respective deposit servers 7 and then the division processing is finished.
  • the deposit servers 7 there are three deposit servers 7 shown in Fig. 1 , and it suffices to deposit the divided data into two of these deposit servers in this case.
  • Q(j,i,k) is given as follows.
  • n 2
  • all of j,i and k only takes a value 1.
  • Q(j,i,k) is given by:
  • c(1,1,1) is defined as 1 so that Q(1,1,1) is defined as R(1).
  • each divided partial data is generated by the following definition formula.
  • D 1 1 S 1 * R 1
  • D 2 1 R 1
  • each divided partial data is generated by the following definition formula.
  • D(1,1) and D(1,2) are generated by the calculation on the original data and the random number, and the content of the original data cannot be ascertained from each one of D(1,1) and D(1,2) alone, but by carrying out the calculation of D(1,1)*D(1,2), it is possible to obtain S(1)*S(2). This is not the same as the original data itself, but it contains no random number component.
  • the random number component When the random number component is eliminated, the following problem arises. Namely, regarding the individual original partial data, if a part of S(2) becomes known, for example, it would become possible to recover a part of S(1) so that it can be considered as not safe.
  • S(2) is a portion containing the header information in that data format or the padding (a part of a data region filled up by 0, for example), etc.
  • this portion may contain keywords or fixed character strings specific to this data format, so that it may become possible to conjecture its content.
  • a part of S(1) may be recovered from the known portion of S(2) and a value of S(1)*S(2).
  • D(3) is the divided data that comprise only the random numbers
  • the property that the original data can be recovered from a prescribed number of the divided data among the n sets of the divided data is still intact as follows.
  • D(3) is the divided data that comprise only the random numbers
  • R(j+2) can be obtained by calculating D(2,j+1)*D(3,j+1) as described above
  • R(j) can be obtained by calculating D(2,j+2)*D(3,j+2) as described above
  • D(4) is the divided data that comprise only the random numbers
  • S can be recovered from two arbitrary divided data D(1) and D(2), or D(2) and D(3), or D(4) and any arbitrary one of the divided data D(1), D(2) or D(3), for which a difference in the number of calculation is one. Namely, if three divided data among the four divided data are acquired, at least one of the above described cases can be realized so that the original data can be recovered from arbitrary three divided data among the four divided data.
  • the case of the division into five is basically the same as the case of the division into four, in all of the case of recovering S by acquiring D(1) and D(2), or D(2) and D(3), the case of recovering S by acquiring D(3) and D(4), and the case of recovering S by acquiring D(5) and any one of D(1), D(2), D(3) and D(4).
  • S can be recovered from two arbitrary divided data D(1) and D(2), or D(2) and D(3), or D(3) and D(4), or D(5) and any arbitrary one of the divided data D(1), D(2), D(3) or D(4), for which a difference in the number of calculation is one. Namely, if three divided data among the five divided data are acquired, at least one of the above described cases can be realized so that the original data can be recovered from arbitrary three divided data among the five divided data.
  • the original data can be recovered from (n+1)/2 sets of the divided data if n is an odd number, or (n/2)+1 sets of the divided data if n is an even number.
  • This number of sets is obtained as one plus the maximum number that can be selected when there are n divided data, the adjacent divided data are not to be selected and the n-th divided data is not to be selected.
  • the maximum number plus one sets of the divided data are acquired, two divided data for which a difference in the number of calculation is one or the n-th divided data and any other divided data are surely contained among them, so that this gives the number of divided data that are necessary for the recovery.
  • the processing procedure of the data division method of the above described embodiment can be recorded on a recording medium such as CD or FD and this recording medium can be incorporated into a computer system.
  • the program recorded on the recording medium can be downloaded into the computer system through a communication channel, or installed into the computer system from the recording medium, and then the computer system can be operated by the program such that the computer system functions as a data division device for realizing the data division method.
  • the distribution of the program can be improved.
  • the prescribed definition formula comprises the exclusive 0R of the original partial data and the random number partial data, so that the high speed and high performance calculation processing power for carrying out the polynomial and residue calculation as required conventionally is not necessary, and it is possible to generate the divided data easily and quickly by repeating a simple calculation processing even with respect to the large capacity data.
  • the original data is recovered by applying the definition formula to the divided data in a number less than the number of division among a plurality of the divided data that are generated, so that the original data can be recovered by the divided data in a prescribed number x which is less than the number of division, and the original data can be recovered even when as many divided data as the number of division minus x are lost or destroyed.
  • the original data is received from the terminal through the network, and the plurality of divided partial data generated by applying the original partial data, random number partial data and divided partial data generation processing with respect to this original data are transmitted to the deposit servers through the network and stored and managed by the deposit servers, so that many users can make accesses from the terminals through the network and make request for the data division, so that the data division device can be shared by many users and can be made economical.
  • the original data is divided by the processing unit bit length into a plurality of original partial data, a plurality of random number partial data are generated, and divided partial data that constitute each divided data are generated according to a prescribed definition formula formed by the exclusive OR of the original partial data and the random number partial data, so that by using a definition formula formed by the exclusive 0R calculation which is a bit calculation suitable for the computer processing rather than the polynomial and the residue calculation conventionally used, it does not require a high speed and high performance calculation processing power, the divided data can be generated easily and quickly even for the large capacity data by repeating the simple calculation processing, and the memory capacity required for maintaining the divided data becomes smaller than the capacity that is linearly proportional to the number of division.
  • the embodiments described above is directed to the case where the divided data include one divided data formed by a random number alone, and one or more divided data formed by the divided partial data generated by the exclusive OR calculation of one original partial data and one or more random number partial data.
  • the divided data include one or more divided data formed by a random number alone, and one or more divided data formed by the divided partial data generated by the exclusive OR calculation of one or more original partial data and one or more random number partial data.
  • the divided data include two or more divided data formed by the divided partial data generated by the exclusive 0R calculation of one or more original partial data and one or more random number partial data.

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  • Engineering & Computer Science (AREA)
  • Computer Security & Cryptography (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Storage Device Security (AREA)
  • Compression, Expansion, Code Conversion, And Decoders (AREA)
  • Information Retrieval, Db Structures And Fs Structures Therefor (AREA)
  • Complex Calculations (AREA)
  • Data Exchanges In Wide-Area Networks (AREA)
EP03780959.7A 2002-12-19 2003-12-19 Secret sharing scheme using exclusive or calculation Expired - Lifetime EP1576763B1 (en)

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PCT/JP2003/016389 WO2004057461A2 (en) 2002-12-19 2003-12-19 Data division method and device using exclusive or calculation

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JP2011041326A (ja) 2011-02-24
JP5194094B2 (ja) 2013-05-08
US7616766B2 (en) 2009-11-10
HK1087859A1 (en) 2006-10-20
WO2004057461A2 (en) 2004-07-08
AU2003288758A1 (en) 2004-07-14
US20060072744A1 (en) 2006-04-06
EP1576763A2 (en) 2005-09-21
CN1726669A (zh) 2006-01-25
CN100563152C (zh) 2009-11-25
AU2003288758A8 (en) 2004-07-14

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